Is it possible for the French head of state to get divorced while in office? The constitution states that the President of the Republic is immune from all legal proceedings, criminal or civil. Does that also apply to divorce? Some constitutional experts said it did. Others disagreed.

The daily drip-drip of speculation on the state of the Sarkozy marriage moved to a new stage yesterday. Two reputable news organisations – the magazine Nouvel Observateur and the 24-hour news channel LCI – reported that the pair had begun formal proceedings on Monday to become the former "first couple".

Le Nouvel Observateur said the Sarkozys had gone together to see a judge in Neuilly-sur-Seine, just west of Paris, on Monday afternoon. It promised a full account in its weekly edition today.

LCI had a somewhat different version of events. The channel said Mme Sarkozy had gone with a lawyer on Monday to see a judge in Nanterre, where the couple have always lived.

It is claimed the lawyer later visited M. Sarkozy at the Elysée Palace.

Reports of an irreconcilable rift in the marriage have been circulating for more than two weeks but French – and foreign – media reporting of the story is limited by the French law which forbids the invasion of privacy.

Mme Sarkozy, 49, once an important part of her husband's political team, has not attended an official state function for more than three months. The Elysée Palace said on Monday that she would not take part in her husband's state visit to Morocco next week.

The causes of the apparent break-down of the President's marriage – five months after he took office – are unclear. The couple separated for 10 months in 2005. Both had relationships with other people before they came back together in January 2006.

Mme Sarkozy was an energetic member of her husband's campaign team early this year before abruptly disappearing from view and failing to turn up to vote for her husband in the second round of the election on 6 May. Since then she has made more news by her non-appearances than her appearances.

She failed to turn up for a hot-dog picnic with President George Bush and family in August and she decided not to travel to Sofia this month after she and her husband were invited to receive the thanks of the Bulgarian people for their efforts to release the Bulgarian nurses held in Libya.

No previous French president or prime minister has divorced while in office. A break-up could affectM. Sarkozy's already-eroding popularity, especially if the French people felt the marriage presented to them during the campaign was a sham. The President, 52, faces one of the first serious challenges to his social and economic reform programme today when a one-day strike against the reduction of special pension rights for rail and other public sector workers will close down train, bus and metro services across France.

Didier Maus, a professor of constitutional law at the Sorbonne, said the debate over the presidential law need not apply to a private lawsuit, such as divorce, so long as both parties agreed.